Numerical modeling of waves for a tsunami early warning system

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xiii 4.13 Panels a and b: absolute values of the Fourier transform coefficients of the water surface elevations at point A, computed with the three dimensional model (thin black line) and with the depth integrated model, without any filter function (thick black line); panels c and d: frequency filter (continuous black lines) and landslide filter (dashed red lines); panels e and f: absolute values of the Fourier transform coefficients of the water surface elevations at point A, computed with the depth integrated model, with the frequency filter (continuous black lines) and with the landslide filter function (dashed red line). . . . . . . . . . . . . . . . . . 58 4.14 Comparison of the free surface elevation obtained from the three dimensional model (dashed red line) and from the long wave depth integrated model respectively using the frequency filter function (thick black line) and the landslide filter function (thin black line).The presented results are relative to the points A (left panels) and B (right panels) of figure 4.10. 59 4.15 Sketch of the computational domain. . . . . . . . . . . . . . . 60 4.16 Comparison of the free surface elevation obtained from the three dimensional model (dashed red line) and that obtained from the depth integrated model with the frequency filter function (continuous black line). The presented results are relative to the points A (left panel) and B (right panel) of figure 4.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.17 Panels a and b: absolute values of the Fourier transform coefficients of the water surface elevations, computed with the three dimensional model (thin black line) and with the depth integrated model, without any filter function (thick black line); panels c and d: absolute values of the Fourier transform coefficients of the water surface elevations, computed with the depth integrated model, with the frequency filter (continuous black lines) and with the landslide filter function (dashed red line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.18 Picture of the physical model at the LIAM laboratory, L’Aquila, Italy. . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.19 Sketch of the landslide used in the experiments. . . . . . . . . 64 4.20 Sketch of the experimental layout of the landslide generated waves over a plane beach experiments. . . . . . . . . . . . . . 65
xiv 4.21 Comparison of the experimental data (red dashed line) and the numerical one (black solid line) . . . . . . . . . . . . . . . 66 4.22 Comparison of the numerical data (thick black line) and the analytical solution one (black thin line) . . . . . . . . . . . . . 67 4.23 Sketch of the layout of the conical island experiments. . . . . . 68 4.24 Pictures of the conical island experiments. Figure taken from the paper of Di Risio et al. (2009b) . . . . . . . . . . . . . . . 69 4.25 Layout of sea-level and run-up gauges position . . . . . . . . . 70 4.26 Numerical domain of the frequency-dispersive model. The numbers 2.07, 4.47 and 8.00 express the radii in meters of the undisturbed shoreline of the island base at the tank bottom and of the external circular boundary respectively . . . . . . . 72 4.27 Comparison of the free surface elevations at the near field gauges position, measured (red dashed line) and obtained from the numerical model (black solid line). The numerical results are achieved by using the registration of the free surface elevation at the gauge 15S to estimate the wave source term. . 74 4.28 Comparison of the free surface elevations at the far field gauges position, measured (red dashed line) and obtained from the numerical model (black solid line). The numerical results are achieved by using the registration of the free surface elevation at the gauge 15S to estimate the wave source term. . . . . . . 75 4.29 Comparison of the free surface elevations at the back field gauges position, measured (red dashed line) and obtained from the numerical model (black solid line). The numerical results are achieved by using the registration of the free surface elevation at the gauge 15S to estimate the wave source term. . 76 4.30 Comparison of the wave energy spectra at gauges 12S (left panel) and 15S (right panel), measured (red dashed line) and obtained from the numerical model (black solid line). The numerical results are achieved by using the registration of the free surface elevation at the gauge 15S to estimate the wave source term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.31 Comparison of the free surface elevations at the near field gauges position, measured (red dashed line) and obtained from the numerical model (black solid line). The numerical results are achieved by using the registration of the free surface elevation at the gauge 12S to estimate the wave source term. . 77
Page 1 and 2: Università degli studi ROMA TRE Ph
Page 3 and 4: To my father Michele, my mother Ant
Page 6 and 7: Abstract A numerical model based on
Page 8 and 9: Sommario Un modello numerico basato
Page 10 and 11: Contents 1 Introduction 3 1.1 Tsuna
Page 12 and 13: List of Figures 1.1 Principal phase
Page 16 and 17: 4.32 Comparison of the free surface
Page 18 and 19: xvii 5.8 Numerical results of the S
Page 20: List of Tables 4.1 Radial and Angul
Page 23 and 24: Numerical modeling of waves for a t
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η1 (m) η2 (m) η3 (m) η4 (m) η5
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Numerical modeling of waves for a t
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η (m) 0.02 0 −0.02 Numerical mod
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aFourier filter functions aFourier
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half an hour. ηS12(m) ηS7(m) ηS1
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ηS6(m) ηS9(m) Numerical modeling
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ηS15(m) ηS24(m) ηS16(m) −0.01
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η(m) η(m) η(m) 50 0 Numerical mo
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η (m) η (m) η (m) η (m) 20 0
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and Numerical modeling of waves for
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Numerical modeling of waves for a tsunami early warning system

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